Example: Find a basis for the null space of the matrix -3 1 2 -1 1 0 0 -1 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Example: Find a basis for the null space of the matrix
-3 1
(3
2 4
2 -1 10
0 -1 0 1
![Definition: For n ≥ 2, the determinant of an n x n matrix A = [a] is the sum of n terms of the form
±a₁jdet Aij, with plus and minus signs alternating, where the entries a11, 12,..., an are from the first row of
A. In other words,
det A = a₁1det A₁1 - a12det A12 + ... + (−1)¹+andet Ain.
2 3 -1
Example: Compute the determinant of 1 2 -3
07 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d4f07e6-ff0e-4dd7-9b82-622a270b91d8%2F51b79583-77fa-48bc-a2ce-5e7b2c8fd3fa%2Fh5y2esq_processed.png&w=3840&q=75)
Transcribed Image Text:Definition: For n ≥ 2, the determinant of an n x n matrix A = [a] is the sum of n terms of the form
±a₁jdet Aij, with plus and minus signs alternating, where the entries a11, 12,..., an are from the first row of
A. In other words,
det A = a₁1det A₁1 - a12det A12 + ... + (−1)¹+andet Ain.
2 3 -1
Example: Compute the determinant of 1 2 -3
07 1
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